A limiting problem for a family of eigenvalue problems involving p-Laplacians

被引：2

作者：

Mihailescu, Mihai ^{[1
,2
]}

Rossi, Julio D. ^{[3
]}

Stancu-Dumitru, Denisa ^{[2
,4
]}

机构：

[1] Univ Craiova, Dept Math, Craiova 200585, Romania

[2] Romanian Acad, Simion Stoilow Inst Math, Res Grp Project PN III P4 ID PCE 2016 0035, Bucharest 010702, Romania

[3] Univ Buenos Aires, FCEyN, Dept Matemat, Ciudad Univ,Pab 1, RA-1428 Buenos Aires, DF, Argentina

[4] Univ Politehn Bucuresti, Dept Math & Comp Sci, Bucharest 060042, Romania

来源：

REVISTA MATEMATICA COMPLUTENSE | 2019年 / 32卷 / 03期

关键词：

Eigenvalue problem; Weak solution; Distance function; Gamma-convergence; Viscosity solution; INFINITY;

D O I：

10.1007/s13163-018-00291-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as p ->infinity, of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.

引用

页码：631 / 653

页数：23

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